A regular body,
in geometry, means one of the five regular solids, called
“Platonic” because first suggested by Plato. (See
To body forth.
To give mental shape to an ideal form.
Imagination bodies forth
The forms of things unknown.
Shakespeare: Midsummer Night's Dream, v.1
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894